1. What is the instantaneous rate of change?
2. Is the graph increasing or decreasing?
3. What are the differences between counting squares and using trapezoids when estimating the definite integral?
1. Understand the instantaneous rate of change.
2, Describe the rate of change given an equation, graph or table.
3, Estimate the definite integral by counting squares.
4. Estimate the definite integral by using trapezoids.
Calculus. Concepts and Applications. Paul A. Foerster.
Test
Chapter 2
Properties of Limits
1. What is limit?
2. How is a limit defined ?
3. How are limits calculated ?
4. How is the concept of limit related to the continuity of a function ?
1. Understand the concept of a limit and graphical behavior.
2, Calculate limits of functions graphically, numerically, and algebraically.
3. Understand the intermediate value theorem.
Derivatives, Antiderivatives, and the Indefinite Integrals
1. What does the derivative of a function at a point mean ?
2. How is the slope of the tangent line related to the derivative of a function at a point?
3. What is the derivative of a function?
4. How are the graph of the function related to the graph of the derivative?
5. How are displacement, velocity and acceleration related?
6. How to differentiate a composite function?
1. Calculate the difference quotient.
2. Interpret the derivative graphically.
3. Determine the equation of a tangent line or a normal line to a function at a point.
4. Evaluate or approximate (where appropriate) f'(c) for a function defined by an equation, a graph or a table.
5. Analyze displacement, velocity and acceleration equations and graphs.
6. Determine derivatives using the power function
7. Evaluate an antiderivative.
8. Learn the derivatives of sine and cosine functions.
9. Calculate the derivative using the chain rule.
10. Find the derivative of an exponential or logartimic function.
Quizzes
Test
Chapter 4
Products, Quotients, and Parametric Functions
(a) Extreme Values of Functions
(b) Mean Value Theorem
(c) Connecting f' and f'' with the Graph of f
(d) Modeling and Optimization
(e) Linearization and Newton's Method
(f) Related Rates
What is the connection between the graph of function f and the graphs of f' and f" ?
If f(t) represents the position of a particle, what do f'(t) and f"(t) represent?
How is the change in the derivative related to the change in the function?
Chapter 5
Definite and Indefinite Integrals
(a) Estimating with Finite Sums
(b) Definite Integrals
(c) Definite Integrals and Antiderivatives
(d) Fundamental Theorem of Calculus
(e) Trapezoidal Rule
Chapter 6
The Calculus of Exponential and Logarithmic Functions
(a) Antiderivatives and Slope Fields
(b) Integration by Substitution
(c) Integration by Parts
(d) Exponential Growth and Decay
(e) Population Growth
(f) Numerical Methods
Chapter 7
The Calculus of Growth and Decay
(a) Integral as Net Change
(b) Areas in the Plane
(c) Volumes
(d) Lengths of Curves
(e) Applications from Science and Statistics
Chapter 8
The Calculus of Plane and Solid Figures
(a) L'Hopital's Rule
(b) Calculus of Parametric Functions
(c) Calculus of Polar Functions
Chapter 9
Algebraic Calculus Techniques for the Elementar Functions
Table of Contents
Chapter 1
2. Is the graph increasing or decreasing?
3. What are the differences between counting squares and using trapezoids when estimating the definite integral?
2, Describe the rate of change given an equation, graph or table.
3, Estimate the definite integral by counting squares.
4. Estimate the definite integral by using trapezoids.
Chapter 2
2. How is a limit defined ?
3. How are limits calculated ?
4. How is the concept of limit related to the continuity of a function ?
2, Calculate limits of functions graphically, numerically, and algebraically.
3. Understand the intermediate value theorem.
Test
Chapter 3
2. How is the slope of the tangent line related to the derivative of a function at a point?
3. What is the derivative of a function?
4. How are the graph of the function related to the graph of the derivative?
5. How are displacement, velocity and acceleration related?
6. How to differentiate a composite function?
2. Interpret the derivative graphically.
3. Determine the equation of a tangent line or a normal line to a function at a point.
4. Evaluate or approximate (where appropriate) f'(c) for a function defined by an equation, a graph or a table.
5. Analyze displacement, velocity and acceleration equations and graphs.
6. Determine derivatives using the power function
7. Evaluate an antiderivative.
8. Learn the derivatives of sine and cosine functions.
9. Calculate the derivative using the chain rule.
10. Find the derivative of an exponential or logartimic function.
Test
Chapter 4
(a) Extreme Values of Functions
(b) Mean Value Theorem
(c) Connecting f' and f'' with the Graph of f
(d) Modeling and Optimization
(e) Linearization and Newton's Method
(f) Related Rates
If f(t) represents the position of a particle, what do f'(t) and f"(t) represent?
How is the change in the derivative related to the change in the function?
Chapter 5
(a) Estimating with Finite Sums
(b) Definite Integrals
(c) Definite Integrals and Antiderivatives
(d) Fundamental Theorem of Calculus
(e) Trapezoidal Rule
Chapter 6
(a) Antiderivatives and Slope Fields
(b) Integration by Substitution
(c) Integration by Parts
(d) Exponential Growth and Decay
(e) Population Growth
(f) Numerical Methods
Chapter 7
(a) Integral as Net Change
(b) Areas in the Plane
(c) Volumes
(d) Lengths of Curves
(e) Applications from Science and Statistics
Chapter 8
(a) L'Hopital's Rule
(b) Calculus of Parametric Functions
(c) Calculus of Polar Functions
Chapter 9